The processor may be supported, but do you have Intel VT and the NX bit turned on in the BIOS? This must be enabled to run 64-bit guests. If it is not enabled, then once you enable and save your BIOS settings, you need to shut down your PC. This will ensure that the settings took. I hope this helps.
Don't forget to use the buttons on the side to award points if you found this useful (you'll get points too).
How do you determine that it's running in 32-bit mode? Remember that the Solaris installer always runs in 32-bit mode, even on 64-bit hardware. Once the installer is finished, the installed system will boot in 64-bit mode. After you've installed, you can confirm it's in 64-bit mode by running "isainfo -b".
BTW, 6/06 (Update 1) is very old. You should probably use the current release (5/08, Update 6) unless you have a specific reason to use an older release.
Thanks for all of the responses. I will try the BIOS options first because they might not be enabled. I checked if it was the 64 bit version by using that command (don't remember of the top of my head) that says how many bits the kernel is using. I'll see if I can get it going today.